How to Use This Book

• Do as many questions as you feel are necessary for you to be confident in your skill. It is best to do all the word problems.
• If you leave out some questions, try doing every second or every third question. Always do some questions from the end of each exercise because the questions usually get harder at the end. You might use the skipped questions for review before a test.
• If you are working on a difficult skill or concept, do half the exercise one day and finish the exercise the next day. That is a much better way to learn.

Self-tests at the end of most topics have an "Aim" at the top. If you do not meet the aim, talk to your instructor, find what is causing the trouble, and do some more review before you go on.

• Write the practice test after you have studied the unit as a practice for the end-of-chapter test, OR
• You might want to write it before you start the unit to find what you already know and which areas you need to work on.

• Step 1: Multiply the ones digit in the large number by the one-digit multiplier.
• Step 2: Multiply the tens digit in the large number by the multiplier.
• Step 3: Multiply the hundreds digit in the large number by the multiplier.
• Step 4: Multiply the thousands digit in the large number by the multiplier.

Exercise 1

1. [latex]\begin{array}{rr}&72\\\times&2\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&81\\\times&5\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&21\\\times&8\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&80\\\times&6\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&73\\\times&3\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&71\\\times&3\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&40\\\times&7\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&90\\\times&9\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&82\\\times&4\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&40\\\times&5\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&92\\\times&4\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&83\\\times&3\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&90\\\times&8\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&71\\\times&9\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&53\\\times&2\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&30\\\times&6\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&81\\\times&7\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&61\\\times&2\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&70\\\times&8\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&41\\\times&6\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&90\\\times&5\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&60\\\times&9\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&92\\\times&3\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&81\\\times&4\\\hline\\\end{array}[/latex]

1. 144
2. 405
3. 168
4. 480
5. 219
6. 213
7. 280
8. 810
9. 328
10. 200
11. 368
12. 249
13. 720
14. 639
15. 106
16. 180
17. 567
18. 122
19. 560
20. 246
21. 450
22. 540
23. 276
24. 324

Exercise 2

1. [latex]\begin{array}{rr}&601\\\times&7\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&423\\\times&3\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&641\\\times&2\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&922\\\times&4\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&820\\\times&4\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&211\\\times&5\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&803\\\times&2\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&542\\\times&2\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&813\\\times&3\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&610\\\times&4\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&901\\\times&6\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&711\\\times&8\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&720\\\times&3\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&910\\\times&5\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&801\\\times&6\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&932\\\times&3\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&731\\\times&2\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&701\\\times&5\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&521\\\times&2\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&632\\\times&3\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&720\\\times&4\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&942\\\times&2\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&710\\\times&9\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&601\\\times&8\\\hline\\\end{array}[/latex]

1. 4207
2. 1269
3. 1282
4. 3688
5. 3280
6. 1055
7. 1606
8. 1084
9. 2439
10. 2440
11. 5406
12. 5688
13. 2160
14. 4550
15. 4806
16. 2796
17. 1462
18. 3505
19. 1042
20. 1896
21. 2880
22. 1884
23. 6390
24. 4808

Renaming and Carrying

Exercise 3

1. [latex]\begin{array}{rr}&16\\\times&8\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&62\\\times&6\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&37\\\times&4\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&14\\\times&9\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&36\\\times&7\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&92\\\times&9\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&48\\\times&6\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&17\\\times&2\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&26\\\times&4\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&54\\\times&7\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&58\\\times&8\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&45\\\times&4\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&56\\\times&3\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&47\\\times&5\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&39\\\times&6\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&75\\\times&6\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&38\\\times&5\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&82\\\times&7\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&98\\\times&3\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&29\\\times&5\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&47\\\times&3\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&74\\\times&8\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&56\\\times&5\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&98\\\times&4\\\hline\\\end{array}[/latex]

1. 128
2. 372
3. 148
4. 126
5. 252
6. 828
7. 288
8. 34
9. 104
10. 378
11. 464
12. 180
13. 168
14. 235
15. 234
16. 450
17. 190
18. 574
19. 294
20. 145
21. 141
22. 592
23. 280
24. 392

Exercise 4

1. [latex]\begin{array}{rr}&648\\\times&9\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&240\\\times&7\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&457\\\times&8\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&404\\\times&2\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&106\\\times&9\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&156\\\times&4\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&407\\\times&8\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&239\\\times&6\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&118\\\times&9\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&425\\\times&7\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&139\\\times&8\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&565\\\times&2\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&248\\\times&3\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&604\\\times&6\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&239\\\times&4\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&576\\\times&3\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&857\\\times&6\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&478\\\times&9\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&674\\\times&7\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&629\\\times&8\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&893\\\times&5\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&583\\\times&8\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&952\\\times&9\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&293\\\times&7\\\hline\\\end{array}[/latex]

1. 5832
2. 1680
3. 3656
4. 808
5. 954
6. 624
7. 3256
8. 1434
9. 1062
10. 2975
11. 1112
12. 1130
13. 744
14. 3624
15. 956
16. 1728
17. 5142
18. 4302
19. 4718
20. 5032
21. 4465
22. 4664
23. 8568
24. 2051

Exercise 5

1. [latex]\begin{array}{rr}&4103\\\times&8\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&6087\\\times&4\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&3280\\\times&6\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&7034\\\times&5\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&8456\\\times&2\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&4758\\\times&7\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&4735\\\times&3\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&5402\\\times&9\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&5394\\\times&4\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&2034\\\times&8\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&8652\\\times&5\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&6392\\\times&7\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&4187\\\times&6\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&1376\\\times&9\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&3297\\\times&2\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&9628\\\times&3\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&7689\\\times&8\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&5160\\\times&3\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&4256\\\times&7\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&5491\\\times&5\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&8032\\\times&9\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&8645\\\times&6\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&6453\\\times&2\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&8129\\\times&4\\\hline\\\end{array}[/latex]

Answers to Exercise 5

1. 32824
2. 24348
3. 19680
4. 35170
5. 16912
6. 33306
7. 14205
8. 48618
9. 21576
10. 16272
11. 43260
12. 44744
13. 25122
14. 12384
15. 6594
16. 28884
17. 61512
18. 15480
19. 29792
20. 27455
21. 72288
22. 51870
23. 12906
24. 32516

Topic A: Self-Test

1. [latex]\begin{array}{rr}&62\\\times&4\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&31\\\times&4\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&423\\\times&3\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&734\\\times&2\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&8342\\\times&2\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&5231\\\times&3\\\hline\\\end{array}[/latex]

1. [latex]\begin{array}{rr}&44\\\times&7\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&69\\\times&8\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&207\\\times&9\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&184\\\times&6\\\hline\\\end{array}[/latex]

1. [latex]\begin{array}{rr}&2834\\\times&5\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&4037\\\times&6\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&9241\\\times&8\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&3652\\\times&4\\\hline\\\end{array}[/latex]

1. Find the products.
   1. 248
   2. 124
   3. 1269
   4. 1468
   5. 16684
   6. 15693
2. Multiply these numbers.
   1. 308
   2. 552
   3. 1863
   4. 1104
3. Find the products.
   1. 14170
   2. 24222
   3. 73928
   4. 14608

Exercise 1

[latex]\begin{array}{rr}&84\\\times&12\\\hline&168\\+&840\\\hline&1008\end{array}[/latex]

1. [latex]\begin{array}{rr}&73\\\times&12\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&50\\\times&42\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&62\\\times&31\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&61\\\times&42\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&91\\\times&53\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&92\\\times&31\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&91\\\times&49\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&72\\\times&48\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&53\\\times&30\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&41\\\times&53\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&42\\\times&94\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&80\\\times&86\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&31\\\times&79\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&54\\\times&40\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&61\\\times&48\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&60\\\times&31\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&55\\\times&73\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&84\\\times&56\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&53\\\times&38\\\hline\\\end{array}[/latex]

Answers to Exercise 1

1. 876
2. 2100
3. 1922
4. 2562
5. 4823
6. 2852
7. 4459
8. 3456
9. 1590
10. 2173
11. 3948
12. 6880
13. 2449
14. 2160
15. 2928
16. 1860
17. 4015
18. 4704
19. 2014

Exercise 2

1. [latex]\begin{array}{rr}&52\\\times&70\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&91\\\times&70\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&83\\\times&70\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&49\\\times&70\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&61\\\times&70\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&16\\\times&70\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&36\\\times&70\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&398\\\times&70\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&432\\\times&70\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&863\\\times&70\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&907\\\times&70\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&503\\\times&70\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&452\\\times&70\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&943\\\times&70\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&248\\\times&70\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&6287\\\times&70\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&9025\\\times&70\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&8907\\\times&70\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&300\\\times&70\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&9075\\\times&70\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&3952\\\times&70\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&1528\\\times&70\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&7106\\\times&70\\\hline\\\end{array}[/latex]

1. 3 640
2. 6 370
3. 5 810
4. 3 430
5. 4 270
6. 1 120
7. 2 520
8. 27 860
9. 30 240
10. 60 410
11. 63 490
12. 35 210
13. 31 640
14. 66 010
15. 17 360
16. 440 090
17. 631 750
18. 623 490
19. 21 000
20. 635 250
21. 276 640
22. 106 960
23. 497 420

Multiplying by Three-Digit Multipliers

Exercise 3

1. [latex]\begin{array}{rr}&416\\\times&213\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&375\\\times&291\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&361\\\times&475\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&275\\\times&863\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&984\\\times&469\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&489\\\times&578\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&498\\\times&123\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&267\\\times&854\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&613\\\times&368\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&725\\\times&547\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&269\\\times&912\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&752\\\times&697\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&983\\\times&357\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&835\\\times&148\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&386\\\times&296\\\hline\\\end{array}[/latex]

1. 88608
2. 109125
3. 171475
4. 237325
5. 461496
6. 282642
7. 61254
8. 228018
9. 225584
10. 396575
11. 245328
12. 524144
13. 350931
14. 123580
15. 114256

1. Count all the zeros at the end of the numbers in both factors.
2. Write down that many zeros at the end of the product.
3. Multiply the other digits in the usual way and put them before the zeros.

Exercise 1

1. [latex]\begin{array}{rr}&300\\\times&20\\\hline&6000\end{array}[/latex]
2. [latex]\begin{array}{rr}&6000\\\times&200\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&210\\\times&20\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&800\\\times&600\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&400\\\times&500\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&6000\\\times&90\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&50000\\\times&6000\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&80000\\\times&30\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&5000\\\times&50\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&70\\\times&80\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&3000\\\times&700\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&50000\\\times&900\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&9000\\\times&8000\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&60000\\\times&90\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&90000\\\times&2000\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&600\\\times&600\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&40000\\\times&800\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&2400\\\times&70\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&390\\\times&40\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&7200\\\times&5000\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&7000\\\times&7000\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&61000\\\times&400\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&5200\\\times&300\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&40\\\times&60\\\hline\\\end{array}[/latex]

1. 6 000
2. 1 200 000
3. 4 200
4. 480 000
5. 200 000
6. 540 000
7. 300 000 000
8. 2 400 000
9. 250 000
10. 5 600
11. 2 100 000
12. 45 000 000
13. 72 000 000
14. 5 400 000
15. 180 000 000
16. 360 000
17. 32 000 000
18. 168 000
19. 15 600
20. 36 000 000
21. 49 000 000
22. 24 400 000
23. 1 560 000
24. 2 400

Topic C: Self-Test

1. [latex]\begin{array}{rr}&600\\\times&70\\\hline\end{array}[/latex]
2. [latex]\begin{array}{rr}&9000\\\times&30\\\hline\end{array}[/latex]
3. [latex]\begin{array}{rr}&5000\\\times&600\\\hline\end{array}[/latex]
4. [latex]\begin{array}{rr}&3000\\\times&500\\\hline\end{array}[/latex]
5. [latex]\begin{array}{rr}&400\\\times&50\\\hline\end{array}[/latex]
6. [latex]\begin{array}{rr}&8000\\\times&1000\\\hline\end{array}[/latex]

1. [latex]\begin{array}{rr}&87\\\times&23\\\hline\end{array}[/latex]
2. [latex]\begin{array}{rr}&268\\\times&25\\\hline\end{array}[/latex]
3. [latex]\begin{array}{rr}&9421\\\times&75\\\hline\end{array}[/latex]
4. [latex]\begin{array}{rr}&2632\\\times&49\\\hline\end{array}[/latex]
5. [latex]\begin{array}{rr}&365\\\times&455\\\hline\end{array}[/latex]
6. [latex]\begin{array}{rr}&7264\\\times&590\\\hline\end{array}[/latex]

Answers to Topic C Self Test

1. 42000
2. 270000
3. 3000000
4. 1500000
5. 20000
6. 8000000

• altogether
• combined
• in all
• total
• the average is
• product
• how many?
• how much?
• each

Exercise 1

1. Maria spent $151 a month to ride to work. How much did it cost her to ride to work for the whole year? (1 year = 12 months)
2. Fred travels 121 km a day on his delivery route. How far does he travel in 5 working days?
3. Manuel buys 340 L of gas a month. In 6 months, how many litres of gas does Manual buy?
4. An apartment building has 16 apartments, each rented for $870 a month. What is the total monthly rental income from this building?
5. A farmer sells potatoes at $53 per 50 kg sack. How much will he get for 75 sacks?
6. Bob is paid $12 per hour. If he worked 39 hours last week and 24 hours this week, how much did he earn for the two weeks? (two operations)
7. It costs $35260 per working day to run the factory. How much does it cost to run this factory for a month of 23 working days?
8. The train has an average speed of 75 km an hour. How far does this train travel in 14 hours?
9. Lee’s sports car averages 18 km per litre. How far can she drive on 12 L of gasoline?
10. Frank bought a used car and paid for it over 15 months. He made 15 monthly payments of $325 each. How much did he pay?

Answers to Exercise 1

1. $1812
2. 605 km
3. 2040 L
4. $13920
5. $3975
6. 63hours, $756
7. $810, 980
8. 1050 km
9. 216 km
10. $4875

Topic D: Self-Test

c. A tanker truck made 275 trips in one year. The truck hauled 23,800 litres each time. How many litres did the truck haul during the year?

1. 1587600 kilograms
2. 42228 kilometres
3. 6545500 litres
4. 400 × 200 = 80000 meals

1. [latex]\begin{array}{rr}&48\\\times&7\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&78\\\times&9\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&892\\\times&8\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&536\\\times&6\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&2375\\\times&4\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&5649\\\times&3\\\hline\\\end{array}[/latex]

C. Find the products.

1. [latex]\begin{array}{rr}&67\\\times&19\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&581\\\times&34\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&7310\\\times&46\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&754\\\times&692\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&2735\\\times&846\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&857\\\times&308\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&629\\\times&407\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&2805\\\times&15\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&5102\\\times&743\\\hline\\\end{array}[/latex]

1. [latex]\begin{array}{rr}&1000\\\times&82\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&100\\\times&26\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&6263\\\times&1000\\\hline\\\end{array}[/latex]
4. 407 × 100 =
5. 100 × 9482 =
6. 3614 × 10 =
7. 1000 × 1795 =

1. [latex]\begin{array}{rr}&50\\\times&40\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&600\\\times&800\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&9000\\\times&500\\\hline\\\end{array}[/latex]

1. [latex]\begin{array}{rr}&68\\\times&39\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&185\\\times&94\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&6763\\\times&69\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&853\\\times&399\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&2735\\\times&846\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&68924\\\times&268\\\hline\\\end{array}[/latex]

1. The Yellow River in China is 5464 kilometres long. How many kilometres will 75 boats cover if they travel the length of the river?
2. Mount Logan in Canada is 5959 metres high. How many metres would 24 climbers cover if they were able to climb to the top of Mt. Logan?
3. How many pieces of candy are needed to pack 500 boxes, if each box has 8 rows and each row has 15 pieces of candy? (2-step question)
4. The distance between Prince Rupert and Kelowna is 1409 km. Estimate how many kilometres 42 trucks will travel if each truck makes one trip.

1. Find the products.
   1. 405
   2. 219
   3. 882
   4. 2048
   5. 18684
   6. 24396
2. Find the products.
   1. 336
   2. 702
   3. 7136
   4. 3216
   5. 9500
   6. 16947
3. Find the products.
   1. 1273
   2. 19754
   3. 336260
   4. 521768
   5. 2313810
   6. 263956
   7. 256003
   8. 42075
   9. 3790786
4. Find the products. Use the shortcut.
   1. 82000
   2. 2600
   3. 6263000
   4. 40700
   5. 948200
   6. 36140
   7. 1795000
5. Find the products. Use the shortcut.
   1. 2000
   2. 480000
   3. 4500000
6. Find an estimated product.
   1. 70 × 40 = 2800
   2. 200  × 90  = 18000
   3. 7000 × 70 = 490000
   4. 900  × 400  =  360000
   5. 3000 × 800 = 2400000
   6. 70000  × 300  =  21000000
7. Word problems.
   1.  409800 kilometres
   2. 143016 metres or 286032 there and back
   3. 60000 pieces of candy
   4. 1000 × 40  =  40000 kilometres

3 × 4 = 12

12 ÷ 4 = 3

Learn this vocabulary for division:

• Dividend – The number or quantity to be divided; the amount altogether.
• Divisor – The number we divide by. The divisor tells us the number of groups or the quantity in each group that the dividend is to be separated into.
• Quotient – (“kw ō shent”) The answer to a division question.

[latex]\begin{array}{r}\text{quotient}\\\text{divisor} \enclose{longdiv}{\text{dividend}}\end{array}[/latex]             [latex]\text{dividend}\div\text{divisor}=\text{quotient}[/latex]

• Find the divisor in the column on the left of the times table chart.
• Run your finger in a straight line across the divisor row until you come to the dividend.
• Go straight up that column and the quotient should be the top number.

Exercise 1

Answers to Exercise 1

Exercise 2

1. 72 ÷ 6 =
2. 12 ÷ 2 =
3. 3 ÷ 1 =
4. 80 ÷ 10 =
5. 18 ÷ 6 =
6. 40 ÷  4 =
7. 21 ÷ 7 =
8. 50 ÷ 5 =
9. 54 ÷ 9 =
10. 8 ÷  2 =
11. 22 ÷ 11 =
12. 45 ÷ 9 =
13. 4 ÷ 4 =
14. 24 ÷  6
15. 81 ÷ 9 =
16. 88 ÷ 8 =
17. 30 ÷ 3 =
18. 12 ÷ 4 =
19. 33 ÷ 3 =
20. 66 ÷ 11 =
21. 20 ÷ 5 =

1. 12
2. 6
3. 3
4. 8
5. 3
6. 10
7. 3
8. 10
9. 6
10. 4
11. 2
12. 5
13. 1
14. 4
15. 9
16. 11
17. 10
18. 3
19. 11
20. 6
21. 4

Exercise 3

1. 90 ÷ 10 =
2. 70 ÷ 7 =
3. 28 ÷ 7 =
4. 32 ÷ 8 =
5. 24 ÷ 3 =
6. 36 ÷ 12 =
7. 84 ÷ 7 =
8. 10 ÷ 2 =
9. 64 ÷ 8 =
10. 6 ÷ 6 =
11. 60 ÷ 12 =
12. 48 ÷ 4 =
13. 72 ÷ 9 =
14. 20 ÷ 10 =
15. 49 ÷ 7 =
16. 48 ÷ 6 =
17. 36 ÷ 9 =
18. 21 ÷ 3 =

1. 9
2. 10
3. 4
4. 4
5. 8
6. 3
7. 12
8. 5
9. 8
10. 1
11. 5
12. 12
13. 8
14. 2
15. 7
16. 8
17. 4
18. 7

Exercise 4

1. 12 ÷ 6 =
2. 27 ÷ 9 =
3. 56 ÷ 7 =
4. 3 ÷ 1 =
5. 20 ÷ 2 =
6. 9 ÷ 3 =
7. 55 ÷ 5 =
8. 14 ÷ 7 =
9. 42 ÷ 6 =
10. 18 ÷ 3 =
11. 88 ÷ 11 =
12. 63 ÷ 9 =
13. 28 ÷ 4 =
14. 6 ÷ 1 =
15. 30 ÷ 5 =
16. 4 ÷ 2 =
17. 7 ÷ 7 =
18. 48 ÷ 12 =

1. 2
2. 3
3. 8
4. 3
5. 10
6. 3
7. 11
8. 2
9. 7
10. 6
11. 8
12. 7
13. 7
14. 6
15. 6
16. 2
17. 1
18. 4

Remainders

[latex]7\div3=2\text{ R}1[/latex]                            [latex]\begin{array}{r}2\text{ R}1\\3 \enclose{longdiv}{7}\hspace{1.3em}\end{array}[/latex]

Example A

Here are 22 cookies. Circle groups of 5. How many groups of 5 in 22? You should have 4 groups with 2 left over.

[latex]22\div5=4\text{ R}2[/latex]                            [latex]\begin{array}{r}4\text{ R}2\\5 \enclose{longdiv}{22}\hspace{1.3em}\end{array}[/latex]

Example B

Here are 66 suns. Make groups of 9. How many groups of 9 in 66? How many groups? 7 How many left over? 3

[latex]66\div9=7\text{ R}3[/latex]                            [latex]\begin{array}{r}7\text{ R}3\\9 \enclose{longdiv}{66}\hspace{1.3em}\end{array}[/latex]

Exercise 5

1. [latex]23\div10=2\text{ R}3[/latex]         [latex]\begin{array}{r}2\text{ R}3\\10 \enclose{longdiv}{23}\hspace{1.3em}\end{array}[/latex]

2. 24 ÷ 7 =
3. 19 ÷ 3 =
4. 39 ÷ 12 =

Exercise 6

1. [latex]5\enclose{longdiv}{28}[/latex]
2. [latex]4\enclose{longdiv}{15}[/latex]
3. [latex]6\enclose{longdiv}{47}[/latex]
4. [latex]9\enclose{longdiv}{37}[/latex]
5. [latex]2\enclose{longdiv}{13}[/latex]
6. [latex]6\enclose{longdiv}{25}[/latex]
7. [latex]8\enclose{longdiv}{75}[/latex]
8. [latex]3\enclose{longdiv}{19}[/latex]
9. [latex]7\enclose{longdiv}{32}[/latex]
10. [latex]4\enclose{longdiv}{9}[/latex]
11. [latex]9\enclose{longdiv}{55}[/latex]
12. [latex]10\enclose{longdiv}{98}[/latex]
13. [latex]3\enclose{longdiv}{26}[/latex]
14. [latex]8\enclose{longdiv}{47}[/latex]
15. [latex]9\enclose{longdiv}{46}[/latex]
16. [latex]6\enclose{longdiv}{43}[/latex]
17. [latex]5\enclose{longdiv}{49}[/latex]
18. [latex]4\enclose{longdiv}{38}[/latex]
19. [latex]2\enclose{longdiv}{19}[/latex]
20. [latex]7\enclose{longdiv}{61}[/latex]
21. [latex]3\enclose{longdiv}{23}[/latex]
22. [latex]8\enclose{longdiv}{78}[/latex]
23. [latex]9\enclose{longdiv}{67}[/latex]
24. [latex]6\enclose{longdiv}{45}[/latex]

1. 5 R3
2. 3 R3
3. 7 R5
4. 4 R1
5. 6 R1
6. 4 R1
7. 9 R3
8. 6 R1
9. 4 R4
10. 2 R1
11. 6 R1
12. 9 R8
13. 8 R2
14. 5 R7
15. 5 R1
16. 7 R1
17. 9 R4
18. 9 R2
19. 9 R1
20. 8 R5
21. 7 R2
22. 9 R6
23. 7 R4
24. 7 R3

Exercise 7

1. 27 ÷ 5 =
2. 13 ÷ 2 =
3. 46 ÷ 9 =
4. 38 ÷ 6 =
5. 61 ÷ 7 =
6. 14 ÷ 5 =
7. 49 ÷ 8 =
8. 28 ÷ 3 =
9. 78 ÷ 8 =
10. 37 ÷ 4 =
11. 67 ÷ 9 =
12. 52 ÷ 6 =
13. 45 ÷ 8 =
14. 25 ÷ 7 =
15. 11 ÷ 3 =
16. 53 ÷ 9 =
17. 19 ÷ 4 =
18. 77 ÷ 8 =
19. 20 ÷ 3 =
20. 11 ÷ 2 =
21. 23 ÷ 5 =
22. 54 ÷ 7 =
23. 87 ÷ 9 =
24. 9 ÷ 4 =

1. 5 R2
2. 6 R1
3. 5 R1
4. 6 R2
5. 8 R5
6. 2 R4
7. 6 R1
8. 9 R1
9. 9 R6
10. 9 R1
11. 7 R4
12. 8 R4
13. 5 R5
14. 3 R4
15. 3 R2
16. 5 R8
17. 4 R3
18. 9 R5
19. 6 R2
20. 5 R1
21. 4 R3
22. 7 R5
23. 9 R6
24. 2 R1

Topic A: Self-Test

1. 63 ÷ 9 =
2. 21 ÷ 7 =
3. 72 ÷ 8 =
4. 65 ÷ 4 =
5. 86 ÷ 4 =
6. 75 ÷ 6 =

1. [latex]6\enclose{longdiv}{59}[/latex]
2. [latex]9\enclose{longdiv}{87}[/latex]
3. [latex]7\enclose{longdiv}{51}[/latex]
4. [latex]8\enclose{longdiv}{76}[/latex]
5. [latex]5\enclose{longdiv}{49}[/latex]
6. [latex]3\enclose{longdiv}{26}[/latex]

Answers to Topic A Self-Test

1. 7
2. 3
3. 9
4. 9
5. 8
6. 8

1. 9 R5
2. 9 R6
3. 7 R2
4. 9 R4
5. 9 R4
6. 8 R2

Divisibility by 2

Exercise 1

1. 22
2. 35
3. 17
4. 10
5. 274
6. 345
7. 639
8. 456
9. 2437
10. 7548
11. 6754
12. 5543

Divisibility by 3

Exercise 2

1. 27
2. 35
3. 81
4. 94
5. 274
6. 581
7. 564
8. 316
9. 3175
10. 1458
11. 1890
12. 3934

Divisibility by 5

Exercise 3

1. 45
2. 84
3. 72
4. 90
5. 800
6. 753
7. 672
8. 355
9. 6009
10. 6375
11. 7020
12. 1704

Exercise 4

Answers to Exercise 4

Exercise 5

Answers to Exercise 5

Divisibility by 9

Exercise 6

1. 538
2. 783
3. 954
4. 762
5. 6213
6. 5742
7. 7083
8. 5738
9. 34937
10. 39402
11. 74124
12. 45683

Exercise 7

Answers to Exercise 7

Exercise 8

Answers to Exercise 8

Exercise 9

Answers to Exercise 9

Topic B: Self-Test

1. Which numbers are divisible by 2?
2. Which numbers are divisible by 3?
3. Which numbers are divisible by 5?
4. Which numbers are divisible by 9?

B. For each number, identify if it is divisible by 2, 3, 5, and 9.

1. 48, 7512, 5534
2. 48, 1467, 7512
3. 925, 2645
4. 1467

1. Divide.
2. Multiply
3. Subtract and compare the remainder to the divisor.
4. Bring down the next digit in the dividend and repeat.

Exercise 1

1. [latex]4\enclose{longdiv}{364}[/latex]
2. [latex]2\enclose{longdiv}{144}[/latex]
3. [latex]5\enclose{longdiv}{455}[/latex]
4. [latex]7\enclose{longdiv}{651}[/latex]
5. [latex]8\enclose{longdiv}{144}[/latex]
6. [latex]2\enclose{longdiv}{166}[/latex]
7. [latex]7\enclose{longdiv}{588}[/latex]
8. [latex]2\enclose{longdiv}{196}[/latex]
9. [latex]5\enclose{longdiv}{230}[/latex]
10. [latex]8\enclose{longdiv}{584}[/latex]
11. [latex]6\enclose{longdiv}{366}[/latex]
12. [latex]4\enclose{longdiv}{244}[/latex]
13. [latex]5\enclose{longdiv}{375}[/latex]
14. [latex]8\enclose{longdiv}{200}[/latex]
15. [latex]2\enclose{longdiv}{628}[/latex]
16. [latex]7\enclose{longdiv}{357}[/latex]
17. [latex]9\enclose{longdiv}{837}[/latex]
18. [latex]8\enclose{longdiv}{248}[/latex]
19. [latex]8\enclose{longdiv}{312}[/latex]
20. [latex]7\enclose{longdiv}{462}[/latex]
21. [latex]5\enclose{longdiv}{295}[/latex]
22. [latex]6\enclose{longdiv}{384}[/latex]
23. [latex]2\enclose{longdiv}{276}[/latex]
24. [latex]4\enclose{longdiv}{372}[/latex]

1. 91
2. 72
3. 91
4. 93
5. 18
6. 83
7. 84
8. 98
9. 46
10. 73
11. 61
12. 61
13. 75
14. 25
15. 314
16. 51
17. 93
18. 31
19. 39
20. 66
21. 59
22. 64
23. 138
24. 93

Exercise 2

1. [latex]7\enclose{longdiv}{721}[/latex]
2. [latex]9\enclose{longdiv}{954}[/latex]
3. [latex]3\enclose{longdiv}{927}[/latex]
4. [latex]3\enclose{longdiv}{621}[/latex]
5. [latex]4\enclose{longdiv}{824}[/latex]
6. [latex]9\enclose{longdiv}{972}[/latex]
7. [latex]7\enclose{longdiv}{714}[/latex]
8. [latex]2\enclose{longdiv}{416}[/latex]
9. [latex]5\enclose{longdiv}{540}[/latex]
10. [latex]6\enclose{longdiv}{654}[/latex]
11. [latex]8\enclose{longdiv}{832}[/latex]
12. [latex]4\enclose{longdiv}{436}[/latex]
13. [latex]5\enclose{longdiv}{515}[/latex]
14. [latex]2\enclose{longdiv}{814}[/latex]
15. [latex]6\enclose{longdiv}{648}[/latex]
16. [latex]8\enclose{longdiv}{856}[/latex]
17. [latex]5\enclose{longdiv}{525}[/latex]
18. [latex]7\enclose{longdiv}{763}[/latex]
19. [latex]9\enclose{longdiv}{945}[/latex]
20. [latex]3\enclose{longdiv}{315}[/latex]
21. [latex]8\enclose{longdiv}{872}[/latex]
22. [latex]4\enclose{longdiv}{416}[/latex]
23. [latex]6\enclose{longdiv}{618}[/latex]
24. [latex]2\enclose{longdiv}{612}[/latex]

1. 103
2. 106
3. 309
4. 207
5. 206
6. 108
7. 102
8. 208
9. 108
10. 109
11. 104
12. 109
13. 103
14. 407
15. 108
16. 107
17. 105
18. 109
19. 105
20. 105
21. 109
22. 104
23. 103
24. 306

One-Digit Divisors with Remainders

Exercise 3

1. [latex]2\enclose{longdiv}{93}[/latex]
2. [latex]3\enclose{longdiv}{52}[/latex]
3. [latex]5\enclose{longdiv}{94}[/latex]
4. [latex]7\enclose{longdiv}{74}[/latex]
5. [latex]4\enclose{longdiv}{95}[/latex]
6. [latex]9\enclose{longdiv}{96}[/latex]
7. [latex]6\enclose{longdiv}{97}[/latex]
8. [latex]8\enclose{longdiv}{99}[/latex]
9. [latex]9\enclose{longdiv}{98}[/latex]
10. [latex]4\enclose{longdiv}{59}[/latex]
11. [latex]6\enclose{longdiv}{76}[/latex]
12. [latex]3\enclose{longdiv}{79}[/latex]
13. [latex]7\enclose{longdiv}{96}[/latex]
14. [latex]5\enclose{longdiv}{57}[/latex]
15. [latex]2\enclose{longdiv}{47}[/latex]
16. [latex]8\enclose{longdiv}{91}[/latex]
17. [latex]7\enclose{longdiv}{89}[/latex]
18. [latex]6\enclose{longdiv}{82}[/latex]
19. [latex]5\enclose{longdiv}{67}[/latex]
20. [latex]2\enclose{longdiv}{85}[/latex]
21. [latex]4\enclose{longdiv}{71}[/latex]
22. [latex]3\enclose{longdiv}{65}[/latex]
23. [latex]9\enclose{longdiv}{92}[/latex]
24. [latex]8\enclose{longdiv}{94}[/latex]

1. 46 R1
2. 17 R1
3. 18 R4
4. 10 R4
5. 23 R3
6. 10 R6
7. 16 R1
8. 12 R3
9. 10 R8
10. 14 R3
11. 12 R4
12. 26 R1
13. 13 R5
14. 11 R2
15. 23 R1
16. 11 R3
17. 12 R5
18. 13 R4
19. 13 R2
20. 42 R1
21. 17 R3
22. 21 R2
23. 10 R2
24. 11 R6

Check Division by Multiplying

1. Multiply the quotient by the divisor.
2. Add on any remainder.

Exercise 4

1. [latex]7\enclose{longdiv}{709}[/latex]
2. [latex]2\enclose{longdiv}{423}[/latex]
3. [latex]5\enclose{longdiv}{538}[/latex]
4. [latex]4\enclose{longdiv}{609}[/latex]
5. [latex]9\enclose{longdiv}{406}[/latex]
6. [latex]6\enclose{longdiv}{125}[/latex]
7. [latex]3\enclose{longdiv}{605}[/latex]
8. [latex]9\enclose{longdiv}{928}[/latex]
9. [latex]3\enclose{longdiv}{962}[/latex]
10. [latex]4\enclose{longdiv}{805}[/latex]
11. [latex]8\enclose{longdiv}{301}[/latex]
12. [latex]2\enclose{longdiv}{807}[/latex]
13. [latex]6\enclose{longdiv}{725}[/latex]
14. [latex]7\enclose{longdiv}{320}[/latex]
15. [latex]9\enclose{longdiv}{140}[/latex]
16. [latex]8\enclose{longdiv}{483}[/latex]
17. [latex]2\enclose{longdiv}{197}[/latex]
18. [latex]6\enclose{longdiv}{307}[/latex]
19. [latex]5\enclose{longdiv}{504}[/latex]
20. [latex]8\enclose{longdiv}{709}[/latex]
21. [latex]7\enclose{longdiv}{876}[/latex]
22. [latex]4\enclose{longdiv}{101}[/latex]
23. [latex]3\enclose{longdiv}{269}[/latex]
24. [latex]5\enclose{longdiv}{473}[/latex]

1. 101 R2
2. 211 R1
3. 107 R3
4. 152 R1
5. 45 R1
6. 20 R5
7. 201 R2
8. 103 R1
9. 320 R2
10. 201 R1
11. 37 R5
12. 403 R1
13. 120 R5
14. 45 R5
15. 15 R5
16. 60 R3
17. 98 R1
18. 51 R1
19. 100 R4
20. 88 R5
21. 125 R1
22. 25 R1
23. 89 R2
24. 94 R3

Topic C: Self-Test

1. [latex]6\enclose{longdiv}{96}[/latex]
2. [latex]4\enclose{longdiv}{92}[/latex]
3. [latex]7\enclose{longdiv}{91}[/latex]
4. [latex]2\enclose{longdiv}{93}[/latex]
5. [latex]5\enclose{longdiv}{94}[/latex]
6. [latex]3\enclose{longdiv}{52}[/latex]

1. [latex]7\enclose{longdiv}{182}[/latex]
2. [latex]8\enclose{longdiv}{736}[/latex]
3. [latex]6\enclose{longdiv}{162}[/latex]
4. [latex]5\enclose{longdiv}{295}[/latex]
5. [latex]4\enclose{longdiv}{184}[/latex]
6. [latex]9\enclose{longdiv}{576}[/latex]

1. [latex]9\enclose{longdiv}{705}[/latex]
2. [latex]4\enclose{longdiv}{257}[/latex]
3. [latex]7\enclose{longdiv}{899}[/latex]
4. [latex]5\enclose{longdiv}{538}[/latex]
5. [latex]8\enclose{longdiv}{876}[/latex]
6. [latex]6\enclose{longdiv}{628}[/latex]

1. Find the quotient.
   1. 16
   2. 23
   3. 13
   4. 46 R1
   5. 18 R4
   6. 17 R1
2. Divide.
   1. 26
   2. 92
   3. 27
   4. 59
   5. 46
   6. 64
3. Divide and show your check for each answer.
   1. 78 R3
   2. 64 R1
   3. 128 R3
   4. 107 R3
   5. 109 R4
   6. 104 R4

When you divide by 1000

1. The ones, tens, and hundreds digits become the remainder.
2.   The other digits stay the same but are three place values less.
   • thousands become ones
   • ten thousands become tens
   • hundred thousands become hundreds

Exercise 7

1. [latex]1000\enclose{longdiv}{2398}[/latex]
2. [latex]1000\enclose{longdiv}{6475}[/latex]
3. [latex]1000\enclose{longdiv}{4835}[/latex]
4. [latex]1000\enclose{longdiv}{63291}[/latex]
5. [latex]1000\enclose{longdiv}{82405}[/latex]
6. [latex]1000\enclose{longdiv}{293591}[/latex]

Three Digit Divisors

Exercise 8

1. [latex]115\enclose{longdiv}{8682}[/latex]
2. [latex]205\enclose{longdiv}{2384}[/latex]
3. [latex]325\enclose{longdiv}{66321}[/latex]
4. [latex]241\enclose{longdiv}{13284}[/latex]
5. [latex]860\enclose{longdiv}{262412}[/latex]
6. [latex]659\enclose{longdiv}{270190}[/latex]

Topic D: Self-Test

1. [latex]185 \div 10 = [/latex]
2. [latex]4\enclose{longdiv}{92}[/latex]
3. [latex]408 \div 50 =[/latex]
4. [latex]72\enclose{longdiv}{6768}[/latex]
5. [latex]67\enclose{longdiv}{5963}[/latex]
6. [latex]53\enclose{longdiv}{4856}[/latex]
7. [latex]91\enclose{longdiv}{8736}[/latex]
8. [latex]265\enclose{longdiv}{133624}[/latex]
9. [latex]606\enclose{longdiv}{26094}[/latex]
10. [latex]1000\enclose{longdiv}{83652}[/latex]

Answers to Topic D Self-Test

1. 18 R5
2. 23
3. 8R8
4. 94
5. 89
6. 91 R33
7. 96
8. 504 R64
9. 43 R36
10. 83 R652

Exercise 1

1. [latex]2 \enclose{longdiv}{6}[/latex]
2. [latex]20 \enclose{longdiv}{60}[/latex]
3. [latex]200 \enclose{longdiv}{600}[/latex]
4. [latex]2000 \enclose{longdiv}{6000}[/latex]
5. [latex]5 \enclose{longdiv}{25}[/latex]
6. [latex]50 \enclose{longdiv}{250}[/latex]
7. [latex]500 \enclose{longdiv}{2500}[/latex]
8. [latex]5000 \enclose{longdiv}{25000}[/latex]
9. [latex]14 \enclose{longdiv}{28}[/latex]
10. [latex]140 \enclose{longdiv}{280}[/latex]
11. [latex]1400 \enclose{longdiv}{2800}[/latex]
12. [latex]14000 \enclose{longdiv}{28000}[/latex]

Exercise 2

1. [latex]30\enclose{longdiv}{90}[/latex]
2. [latex]40\enclose{longdiv}{1600}[/latex]
3. [latex]300\enclose{longdiv}{1200}[/latex]
4. [latex]400\enclose{longdiv}{20000}[/latex]
5. [latex]500\enclose{longdiv}{35000}[/latex]
6. [latex]700\enclose{longdiv}{42000}[/latex]
7. [latex]60000\enclose{longdiv}{2400000}[/latex]
8. [latex]800000\enclose{longdiv}{400000000}[/latex]

Rounding Division Questions to Estimate

1. If the divisor only has one digit, do not round it,
2. Round the dividend to make the arithmetic easier for yourself.

Exercise 3

1. [latex]365\enclose{longdiv}{27692}[/latex]
2. [latex]23\enclose{longdiv}{34459}[/latex]
3. [latex]45\enclose{longdiv}{4590}[/latex]
4. [latex]16\enclose{longdiv}{6729}[/latex]
5. [latex]56\enclose{longdiv}{4792}[/latex]
6. [latex]75\enclose{longdiv}{7648}[/latex]
7. [latex]81\enclose{longdiv}{4049}[/latex]
8. [latex]68\enclose{longdiv}{5636}[/latex]
9. [latex]19\enclose{longdiv}{1672}[/latex]
10. [latex]200\enclose{longdiv}{20000}[/latex]
11. [latex]557\enclose{longdiv}{41680}[/latex]

Topic E: Self-Test

1. [latex]98\enclose{longdiv}{8541}[/latex]
2. [latex]27\enclose{longdiv}{2963}[/latex]
3. [latex]241\enclose{longdiv}{26348}[/latex]
4. [latex]55\enclose{longdiv}{3276}[/latex]
5. [latex]24\enclose{longdiv}{1776}[/latex]
6. [latex]59\enclose{longdiv}{11830}[/latex]

1. 8500 ÷ 100 = 85
2. 3000 ÷ 30 =100
3. 26000 ÷ 200 =130
4. 3000 ÷ 60 = 50
5. 2000 ÷ 20 = 100
6. 12000 ÷ 60 = 200

“Find the average” is another way of asking you to find the amount for one.

•  Look at the question in the problem. What do you have to find out? Look for the words “per” and “for one.”
• How will the answer be written? That is your clue. If the answer is km/h then the division equation will be total km ÷ h.  Study these examples:
  • [latex]\text{total of kilometres} \div \text{number of hours} = km/h[/latex]
  • [latex]\text{total of kilometres} \div \text{number of litres} = km/L[/latex]
  • [latex]\text{total cost} \div \text{unit} = \text{cost per unit}[/latex]
  • [latex]\text{total pay} \div \text{hours (or days, etc.)} = \text{pay per hour}[/latex]
  • [latex]\text{total rent}\div \text{number of months} = \text{rent/month}[/latex]
  • [latex]\text{total things done} \div \text{total time} = \text{number done/unit of time}[/latex]
• Do a quick estimate.
•  Look at your estimate  and  re-read the problem. Does your answer make sense?

Average = Total amount  number of items that make the total

• 1 minute = 60 seconds
• 1 hour = 60 minutes
• 1 year = 365 days
• 1 year = 12 months
• 1 year = 52 weeks

• Find the average
• Separated
• Find the ____ per ____
• Split
• Find the unit price
• Shared

Exercise 1

1. A machine shop can stamp out 360 car parts in an 8 hour working How many parts is that per hour?
2. Izyan paid $560 for 4 tires. How much did each tire cost?
3. Bjork earned $8840 in 4 months.
   1. How much did he earn each month?
   2. How much did he earn per week? (4 months is 17 weeks)
4. Theron used 9 L of gasoline to drive 207 km. How many kilometres did he drive per litre?
5. The total cost of the car Elena bought is $14880 including taxes and interest. She will pay for it in 24 equal payments. How much will each payment be?

1. 45 parts per hour
2. $140 per tire
   1. $2210 per month
   2. $520 per week
3. 23 km/L
4. $620 per payment
5. $9 per hour
6. $1245 per month

Exercise 2

1. A train travels 90 km per hour. How many hours will it take the train to go 540 km?
2. A car gets 16 km per litre of gasoline. How many litres will the car need to go 128 km?
3. About 8 m is needed for one parking space. How many parking spaces can be made along a street that is 232 m long?
4. If you spend an average of 8 minutes on one math problem, how many problems can you finish in one hour? Will you have any time left?  How much?
5. The Skating Club members decided to sell home-made candy to raise money. The boxes they bought will hold 45 pieces of candy. If everyone makes a double batch of fudge they will have 2590 pieces of How many boxes can they fill? How many pieces of fudge are left-over for them to eat?
6. A class of 334 students is going to Victoria by bus. Each bus holds 43 passengers. How many buses do they need? Will there be any empty seats? (Be careful with this one!)

1. 6 hours
2. 8 L
3. 29 parking spaces
4. 7 problems, yes, 4 min
5. 57 boxes, 25 pieces left over
6. 8 buses, 10 empty seats

Unit Pricing

Exercise 3

1. 2 CDs for $26
2. 3 cans of dog food for $6
3. 4 air fresheners for $8
4. 2 cat treats for $4
5. 2 pizzas for $22
6. 2 cans of peanuts for $8
7. 2 ice cream for $12
8. 4 boxes of chocolate bars for $48
9. 2 WD-40 for $6
10. 3 paint rollers for $9
11. 4 tie downs for $20
12. 3 boxes of diapers for $51
13. 3 work shirts for $45
14. 8 pairs of socks for $64

1. $13
2. $2
3. $2
4. $2
5. $11
6. $4
7. $6
8. $12
9. $3
10. $3
11. $5
12. $17
13. $15
14. $8

Best Buy

Exercise 4

1. 2 L of engine oil for $8 or 5 L of engine oil for $15
2. 4 tires for $240 or 2 tires for $110
3. 6 jars of salad dressing for $24 or 3 jars of salad dressing for $15
4. 7 kg of dog food for $21or 16 kg of dog food for $32
5. 3 DVDs for $54 or 7 DVDs for $119
6. 3 L of laundry soap for $6 or 17 L of laundry soap for $68

Answers to Exercise 4

1. $4, $3, 5 L for $15 is the best buy.
2. $60, $55, 2 tires for $110 is the best buy.
3. $4, $5, 6 salad dressing for $24 is the best buy.
4. $3, $2, 16 kg for $32 is the best buy.
5. $18, $17, 7 DVDs for $119 is the best buy.
6. $2, $4, 3 L for $6 is the best buy.

Topic F: Self Test

1. Enrique drove the 1 920 km from Dease Lake to Creston in 24 hours. What was his average speed in kilometres per hour?
2. The Evergreen Company employs 26 people. Its total payroll for last month was $84 162.  What was the average monthly pay cheque per person?
3. The proud gardener grew a total crop of 135 cucumbers on 15 plants. What was the average crop per plant?
4. In a recent truckload sale, electric stoves were sold for $432. The gross income from the stove sale was $42336.  How many stoves were sold?
5. The 39 farmers in Jones Valley had a total income last year of $2905500. What was their average income?
6. A store has an inventory (stock on hand) of chairs with a total value of $1738. Each chair is to be sold at $79.  How many of these chairs are there?

Answers to Topic F Self-Test

1. 80 km/h
2. $3237 per month
3. 9 cucumbers per plant
4. 98 stoves
5. $74500
6. 22 chairs

Exercise 1

1. Saika gave her students cinnamon hearts on Valentine’s Day. She bought a box of 1120 cinnamon hearts and gave each student 35 candies, using up the whole box. How many students does she have?
2. Each stamp cost 57 cents. Dolores bought 100 stamps. How much money did she spend on stamps (before taxes)?
3. Etienne planted 30 tomato plants in rows of 5 plants.  How many rows did he plant?
4. There are 8 servings per large economy-size can of fruit. The restaurant ordered 5 cases with 24 cans per case. How many servings of fruit can the restaurant get from this order? (This is a two step problem – first find the total number of cans. Then find the number of servings.)
5. A train traveled 2250 km at a speed of 75 km per hour. How many hours did the trip take?
6. The regular mountain bike costs $499 and the fancy model is $675. How much more do you pay for the fancy mountain bike?
7. The members of the Shiny Wheels Bicycle Club ride at an average speed of 16 km/h. On their weekend trip they rode 2 hours Friday night, 7 hours on Saturday, spent two hours soaking their aching bones at the Hot Springs, and then rode a final five hours on Sunday.  How many kilometres did they ride on this weekend trip?  (2 steps)
8. Last week Mrs. Sanderson drove 29 km on Monday, 42 km on Tuesday, 5 km on Wednesday, and 21 km on Friday.  How far did she drive last week?

1. 32 students
2. $57.00
3. 6 rows
4. 960 servings
5. 30 hours
6. $176 more
7. 224 km
8. 97 km

B. Give the answer.

1. [latex]56\div7=[/latex]
2. [latex]40\div8=[/latex]
3. [latex]54\div9=[/latex]
4. [latex]6\enclose{longdiv}{42}[/latex]
5. [latex]9\enclose{longdiv}{72}[/latex]
6. [latex]8\enclose{longdiv}{32}[/latex]

1. [latex]7\enclose{longdiv}{68}[/latex]
2. [latex]4\enclose{longdiv}{29}[/latex]
3. [latex]5\enclose{longdiv}{24}[/latex]
4. [latex]6\enclose{longdiv}{53}[/latex]

1. [latex]8\enclose{longdiv}{296}[/latex]
2. [latex]6\enclose{longdiv}{252}[/latex]
3. [latex]4\enclose{longdiv}{732}[/latex]
4. [latex]5\enclose{longdiv}{175}[/latex]

1. [latex]3\enclose{longdiv}{86}[/latex]
2. [latex]4\enclose{longdiv}{97}[/latex]
3. [latex]2\enclose{longdiv}{71}[/latex]
4. [latex]5\enclose{longdiv}{59}[/latex]

1. [latex]7\enclose{longdiv}{615}[/latex]
2. [latex]2\enclose{longdiv}{647}[/latex]
3. [latex]3\enclose{longdiv}{781}[/latex]
4. [latex]9\enclose{longdiv}{839}[/latex]

1. [latex]8956\div42=[/latex]
2. [latex]32\enclose{longdiv}{832}[/latex]
3. [latex]69140\div56=[/latex]
4. [latex]312\enclose{longdiv}{9984}[/latex]
5. [latex]41082\div334=[/latex]
6. [latex]781\enclose{longdiv}{39752}[/latex]
7. [latex]275\enclose{longdiv}{55661}[/latex]
8. [latex]307\enclose{longdiv}{91838}[/latex]

1. [latex]1000\enclose{longdiv}{38645}[/latex]
2. [latex]18592\div100=[/latex]
3. [latex]4923\div10=[/latex]
4. [latex]100\enclose{longdiv}{17342}[/latex]

J. Quickly find the quotients. Remember to cancel the same number of zeros in both the divisor and dividend in each question.

1. [latex]200\enclose{longdiv}{50000}[/latex]
2. [latex]6000\enclose{longdiv}{360000}[/latex]
3. [latex]40000\enclose{longdiv}{1600000}[/latex]
4. [latex]70000\enclose{longdiv}{6300000}[/latex]

1. [latex]37\enclose{longdiv}{15725}[/latex]
2. [latex]54\enclose{longdiv}{8478}[/latex]
3. [latex]768\enclose{longdiv}{63721}[/latex]
4. [latex]6267\enclose{longdiv}{536497}[/latex]

1. At the Kaizen Factory, 14325 cars were put together in 5 days. Each day the same number of cars were built. How many cars were built each day?
2. The Blaster Rubber Company needs to make 6912 hockey pucks. Mr. Frost, the foreman, says that their machines can make the pucks in 12 hours. How many pucks would be made in one hour?
3. The distance between Fort St. John and Kimberley is 1092 km. What was your average speed if the trip took 12 hours?
4. The new stadium has 15981 seats divided evenly into 76 sections. Estimate how many seats are in each section?

M. Solve the cost per unit price.

1. 4 rolls of hockey tape for $8
2. 4 cans of butane fuel for $12

1. 2 L of antifreeze for $6 or 5 L of antifreeze for $10
2. 8 kilograms of bird seed for $16 or 4 kilograms of bird seed for $12

1. The bakery uses 43 kilograms of butter in each batch of shortbread cookies. How many batches of shortbread can be made from 3569 kilograms of butter?
2. Each crate that the men unloaded weighed 175 kilograms. If they unloaded 232 crates, how many kilograms did they unload?
3. The parts factory produced 4173 less parts this month than last month. The factory produced 49736 parts this month. How many parts did the factory produce last month?
4. Three Eastjet jets were flown 24826 kilometres, 9423 kilometres and 56015 kilometres. What is the total kilometres the three jets were flown?

Answers to Unit 2 Review

1. 1. 8
   2. 5
   3. 6
   4. 7
   5. 8
   6. 4

1. 1. 9 R5
   2. 7 R1
   3. 4 R4
   4. 8 R5

1. 1. 37
   2. 42
   3. 183
   4. 35

1. 1. 28 R2
   2. 24 R1
   3. 35 R1
   4. 11 R4

1. 1. 87 R6
   2. 323 R1
   3. 260 R1
   4. 93 R2

1. 1. 213 R10
   2. 26
   3. 1234 R36
   4. 32
   5. 123
   6. 50 R702
   7. 202 R111
   8. 299 R45

1. 1. 38 R645
   2. 185 R92
   3. 492 R3
   4. 173 R42

1. 1. 250
   2. 60
   3. 40
   4. 90

1. 1. [latex]1600 \div 40=400[/latex]
   2. [latex]8500\div50=170[/latex]
   3. [latex]64000\div800=80[/latex]
   4. [latex]540000\div6000=90[/latex]

1. 1. 2865 cars per day
   2. 576 pucks per hour
   3. 91 km per hour
   4. [latex]16000\div80=200[/latex] 200 seats per section

1. 1. $2
   2. $3

1. 1. $3, $2, 5 L of antifreeze for $10 is the best buy
   2. $2, $3, 8 kilograms of bird seed for $16 is the best buy

1. 1. 83 batches
   2. 40600 kilograms
   3. 53909 parts
   4. 90264 kilometres